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= t1 [0, -1/3, 0, 1] (page cut off) Removed from the final exam. Corrections are change R^4 to to R^5 and text "of the matrix" to "of some matrix" x x x Solution: Find the RREF of A. It has 2 pivots. No test applies to prove the columns are independent, because the columns of A are dependent. Also possible: Apply the Kernel Theorem, which says that a system of linear homogeneous algebraic equations has solution set which is a subspace. Checked with maple. The answer given here is correct. An eigenspace may have multiple vectors found as Strang's Special solutions which are not orthogonal. Gram-Schmidt is applied to these vectors to replace the eigenspace basis by an orthogonal basis.